Small spacecraft have recently emerged as an attractive and highly capable platform that enable scientists and engineers to perform missions of ever-increasing complexity. The popularity of these spacecraft can be attributed in part to the falling cost of development, miniaturization of complex electronics, shortened development life cycles, and increasingly routine access to space as rideshare/secondary payloads. The total cost for flying a small satellite mission is often orders of magnitude lower than a traditional large and more capable counterpart, allowing a growing number of worldwide participants from academia, government, and commercial industries. Given the increased popularity of small spacecraft, lowering costs, and routine access to space, the small satellite industry is poised to produce spacecraft in large quantities and field constellations of considerable size.
There exist many distributed ground station networks servicing a growing population of satellites. Traditional architectures have been established for many decades and consist of globally-dispersed radio frequency (RF) apertures that service spacecraft in all regimes, characterized by LEO, medium Earth orbit (MEO), geosynchronous/geostationary Earth orbit (GEO), and deep space. The ground station networks are responsible for operating a disaggregated population of small satellites with unique requirements such as custom tailored C2 software, different radio frequencies, waveforms, and data protocols, and varying constraints on timeliness for the mission stakeholders. Traditionally, a large team of operators are trained to factor these constraints into deconflicting assets to keep the missions on track. This process is labor-intensive and does not scale to populations of satellites in the hundreds or more given the number of deconfliction events that would need to be considered every day. The nature of small satellite missions is that they are cost constrained, and as such, automated mission operations show the greatest promise for keeping costs down while servicing a vast number of diverse satellites performing separate missions.
The problem of optimizing space-ground communications has been well-studied in recent years as the population of spacecraft and their user base has increased. Typical approaches to usage optimization has involved event deconfliction and task scheduling; techniques which address an oversubscription scheduling problem. Though some processes can be automated, they remain largely overseen by human schedulers who arbitrate complex requests with various organizations to ensure that all conflicts are resolved with enough time for the users to prepare for their schedule slot (i.e. 24-48 hours). There are many quantitative factors to consider including the orbital mechanics that enable opportunities to communicate with a ground station network, link requirements, and efficiency of the communication for both spacecraft and ground station. In addition, there exists a qualitative arbitration process that is generally difficult to quantify and model as it involves potential sensitivities such as customer rank, mission and security classification, experiment timeliness, funding, and many others.
In general, satellite communication planning and scheduling can be framed as a constrained hybrid dynamic optimization problem where the variables are discrete, continuous, dynamic, and constrained. Typical solution strategies involve forming and solving a graph problem. Thus, even a simplified version of this problem cannot be solved in nondeterministic polynomial time, also called NP-hard. In other words, it falls into a class of problems that are too complex to be solved in a realistic amount of time. Most attempts to solve this NP-hard problem approach it with a combination of graph theory and heuristics to create simplifications necessary to converge on a solution. This leads to a degree of conservatism that is contrary to the requirements of large-scale systems. The traditional means of solving the problem broadly apply across the various graph-theoretical algorithms described above and are as follows:                Step 1: Reduce the task requisition cardinality by applying heuristics where possible. This produces a subgraph with lowered complexity.        Step 2: Choose a simple closed-form solution for spacecraft attitude maneuvering so as to reduce the hybrid dynamic problem of Step 1 to a nondynamic but time-dependent graph problem.        Step 3: The problem of Step 2 is divided into separate problems of planning and scheduling. Each problem is then solved using heuristics and graph-theoretic algorithms which generate a solution to the scheduling subproblem based on a given payoff function (e.g. profit).        Step 4: The scheduling sequence from Step 3 is simulated by a high-fidelity propagator. If the test fails, the entire process or parts of the process are repeated until a desirable solution is obtained for flight operations.        
It would be advantageous to provide a mission planning system which solves the scheduling and planning problem by utilizing the application of well-established pseudospectral techniques to a different formulation of the same problem. By considering the problem as a single integrated dynamic optimization problem, many of the heuristics, simplification steps, and iterative loops typically required could be subsequently eliminated. It would be further advantageous to represent the non-smooth problem as smooth and time-continuous, so that the resulting solution could satisfy static and dynamic constraint satisfaction at its first solution.
These and other objects, aspects, and advantages of the present disclosure will become better understood with reference to the accompanying description and claims.